Topological String Theory on Compact Calabi-Yau: Modularity and Boundary Conditions

Abstract

The topological string partition function Z=exp(lambda^{2g-2} F_g) is calculated on a compact Calabi-Yau M. The F_g fulfill the holomorphic anomaly equations, which imply that Z transforms as a wave function on the symplectic space H^3(M,Z). This defines it everywhere in the moduli space of M along with preferred local coordinates. Modular properties of the sections F_g as well as local constraints from the 4d effective action allow us to fix Z to a large extend. Currently with a newly found gap condition at the conifold, regularity at the orbifold and the most naive bounds from Castelnuovos theory, we can provide the boundary data, which specify Z, e.g. up to genus 51 for the quintic.

LaTeX, 57 pages, 2 eps-figures

References in corpus (22)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Massless Black Holes and Conifolds in String Theory
• Black Hole Attractors and the Topological String
• Topological Strings and Integrable Hierarchies
• Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,
• c=1 String as the Topological Theory of the Conifold
• Quantum Background Independence In String Theory
• Hartle-Hawking Wave-Function for Flux Compactifications
• Topological String Partition Functions as Polynomials
• A Farey Tail for Attractor Black Holes
• Counting higher genus curves in a Calabi-Yau manifold
• Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Chern-Simons Gauge Theory As A String Theory
• Strong Coupling Singularities and Non-abelian Gauge Symmetries in $N=2$ String Theory
• Hypermultiplets and Topological Strings
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Attractors and the Holomorphic Anomaly
• Local Mirror Symmetry at Higher Genus
• Topological wave functions and heat equations
• Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface

Cited by in corpus (22)

• D-brane Deconstructions in IIB Orientifolds
• Direct Integration of the Topological String
• Integrability of the holomorphic anomaly equations
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Large Volume Axionic Swiss-Cheese Inflation
• The Witten equation, mirror symmetry and quantum singularity theory
• Evidence for Tadpole Cancellation in the Topological String
• "Finite" Non-Gaussianities and Tensor-Scalar Ratio in Large Volume Swiss-Cheese Compactifications
• Finiteness and the Emergence of Dualities
• On solutions to Walcher's extended holomorphic anomaly equation
• On Sp_4 modularity of Picard--Fuchs differential equations for Calabi--Yau threefolds (with an appendix by Vicentiu Pasol)
• Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
• Topological Strings on Elliptic Fibrations
• On 'Light' Fermions and Proton Stability in 'Big Divisor' D3/D7 Swiss Cheese Phenomenology
• Towards Large Volume Big Divisor D3-D7 "mu-Split Supersymmetry" and Ricci-Flat Swiss-Cheese Metrics, and Dimension-Six Neutrino Mass Operators
• Holomorphic Anomaly in Gauge Theory on ALE space
• A global mirror symmetry framework for the Landau-Ginzburg/Calabi-Yau correspondence
• "Big" Divisor D3/D7 Swiss Cheese Phenomenology
• On Issues in Swiss Cheese Compactifications
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Geometry As Seen By String Theory
• Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I